People frequently gesture when problem-solving, particularly on tasks that require spatial transformation. Gesture often facilitates task performance by interacting with internal mental representations, but how this process works is not well understood. We investigated this question by exploring the case of mental abacus, a technique in which users not only imagine moving beads on an abacus to compute sums, but also produce movements in gestures that accompany the calculations. Because the content of MA is transparent and readily manipulated, the task (...) offers a unique window onto how gestures interface with mental representations. We find that the size and number of MA gestures reflect the length and difficulty of math problems. Also, by selectively interfering with aspects of gesture, we find that participants perform significantly worse on MA under motor interference, but that perceptual feedback is not critical for success on the task. We conclude that premotor processes involved in the planning of gestures are critical to mental representation in MA. (shrink)

Reasoning about ulterior motives was investigated among children ages 6–10 years (total N = 119). In each of two studies, participants were told about children who offered gifts to peers who needed help. Each giver chose to present a gift in either a public setting, which is consistent with having an ulterior motive to enhance one's reputation, or in a private setting, which is not consistent with having an ulterior motive. In each study, the 6- to 7-year olds showed no (...) evidence of understanding that the public givers might have ulterior motives, but the 8- to 10-year olds rated the private givers more favorably. In , the older children were more likely than the younger children to refer to impression management when explaining their judgments of the givers. The younger children who mentioned impression management did so to justify a preference for public givers (e.g., by explaining that public givers are nicer because more of their peers will know that they are nice). Results from suggest that developmental change in children's reasoning about intentions and social outcomes contributes to their understanding of ulterior motives. (shrink)

Previous accounts of how people develop expertise have focused on how deliberate practice transforms the cognitive and perceptual representations and processes that give rise to expertise. However, the likelihood of developing expertise with a particular tool may also depend on the degree to which that tool fits pre‐existing perceptual and cognitive abilities. The present studies explored whether the abacus—a descendent of the first human computing devices—may have evolved to exploit general biases in human visual attention, or whether developing expertise with (...) the abacus requires learning special strategies for allocating visual attention to the abacus. To address this question, we administered a series of visual search tasks to abacus experts and subjects who had little to no abacus experience, in which search targets and distractors were overlaid atop abacus “beads.” Across three studies, we found that both experts and naïve subjects were faster to detect targets in semantically relevant components of the abacus, suggesting that abacus training is not required to exhibit attentional biases toward these components of the abacus. This finding suggests that the attentional biases that scaffold numerical processing of the abacus may emerge from general properties of visual attention that are exploited by the design of the abacus itself. (shrink)

Though there are holes in the theory of how children move through stages of numerical competence, the current approach offers the most promising avenue for characterizing changes in competence as children confront new mathematical concepts. Like the science of mathematics, children's discovery of number is rooted in intuitions about sets, and not purely in analytic truths.

By around the age of 5½, many children in the United States judge that numbers never end, and that it is always possible to add 1 to a set. These same children also generally perform well when asked to label the quantity of a set after one object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: Every natural number, n, has a successor, n (...) + 1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language‐specific counting routines (e.g., the rules in English that represent base‐10 structure). We tested 4‐ and 5‐year‐old children’s knowledge of counting with three tasks, which we then related to (a) children’s belief that 1 can always be added to any number (the successor function) and (b) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge was not directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as 4 years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end. (shrink)

Do children understand how different numbers are related before they associate them with specific cardinalities? We explored how children rely on two abstract relations – contrast and entailment – to reason about the meanings of ‘unknown’ number words. Previous studies argue that, because children give variable amounts when asked to give an unknown number, all unknown numbers begin with an existential meaning akin to some. In Experiment 1, we tested an alternative hypothesis, that because numbers belong to a scale of (...) contrasting alternatives, children assign them a meaning distinct from some. In the “Don’t Give-a-Number task”, children were shown three kinds of fruit (apples, bananas, strawberries), and asked to not give either some or a number of one kind (e.g. Give everything, but not [some/five] bananas). While children tended to give zero bananas when asked to not give some, they gave positive amounts when asked to not give numbers. This suggests that contrast – plus knowledge of a number’s membership in a count list – enables children to differentiate the meanings of unknown number words from the meaning of some. Experiment 2 tested whether children’s interpretation of unknown numbers is further constrained by understanding numerical entailment relations – that if someone, e.g. has three, they thereby also have two, but if they do not have three, they also do not have four. On critical trials, children saw two characters with different quantities of fish, two apart (e.g. 2 vs. 4), and were asked about the number inbetween – who either has or doesn’t have, e.g. three. Children picked the larger quantity for the affirmative, and the smaller for the negative prompts even when all the numbers were unknown, suggesting that they understood that, whatever three means, a larger quantity is more likely to contain that many, and a smaller quantity is more likely not to. We conclude by discussing how contrast and entailment could help children scaffold the exact meanings of unknown number words. (shrink)

Word learning depends critically on the use of linguistic context to constrain the likely meanings of words. However, the mechanisms by which children infer word meaning from linguistic context are still poorly understood. In this study, we asked whether adults (n = 58) and 2‐ to 6‐year‐old children (n = 180) use discourse coherence relations (i.e., the meaningful relationships between elements within a discourse) to constrain their interpretation of novel words. Specifically, we showed participants videos of novel animals exchanging objects. (...) These videos were accompanied by a linguistic description of the events in which we manipulated a single word within a sentence (and vs. because) in order to alter the causal and temporal relations between the events in the discourse (e.g., “One animal handed the baby to the other animal [and/because] the baby started crying in the talfa's arms”). We then asked participants which animal (the giver or the receiver) was the referent of the novel word. Across two experiments, we found evidence that young children used the causal and temporal relations in each discourse to constrain their interpretations of novel words. (shrink)